“[The proof] looked too good to be true ... Something this short and simple — it should have been in textbooks already. So my first thought was, no, this can’t be true.” -Terrance Tao
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Absolutely Amazing Physicists (!) discover a new fundamental and amazing mathematical fact: You can get the Eigenvectors of a matrix using ONLY its Eigenvalues https://arxiv.org/pdf/1908.03795.pdf …pic.twitter.com/Mt797mmqDk
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Here's how much of a badass Terrance Tao is. Upon being contacted by the Particle Physicists (
), Terence Tao came up with three independent proofs in two hoursShow this thread -
The condition on the matrix A is that it be Hermitian, meaning that it is equal to its complex conjugate transpose.
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Some people are commenting without clicking the link. For the click-averse: Terrance Tao is a co-author of this paper
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I can do a more technical & separate thread on this to make the theorem statement more precise if you'd like
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Apparently an equivalent result has been used/discovered before, but as Terry Tao states it was never published. ... oopspic.twitter.com/i08oAEjMqW
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The quote from Terence Tao is from an interview by
@nattyover, from Quantum Magazine. My apologies to Natalie for not citing this properly.https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/ …Show this thread
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What is new here ?
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??? the fact that eigenvalues alone determine the eigenvectors!
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I don’t think this is what the paper says, though?
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yea it does .. the condition on the matrix is that it be hermitian
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